Laying down the law

(Dec 14, 2010)

In actuarial terminology, a mortality "law" is simply a parametric formula used to describe the risk.  A major benefit of this is automatic smoothing and in-filling for areas where data is sparse.  A common example in modern annuity portfolios is that there is often plenty of data up to age 75 (say), but relatively little data above age 90.

For example, if we use a parametric formula like the Gompertz law:

log μx = α + βx

then we can use a procedure like the method of maximum likelihood to estimate α and β.  Once we have these values, we can generate mortality rates at any age we require, not just the ages at which we have data.

But which mortality law should one use?  In a recent paper (Richards,

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Tags: log-likelihood, mortality law, CMI, Gompertz-Makeham family

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